Ricci curvature and Einstein metrics on aligned homogeneous spaces
| Autor: | Lauret, Jorge, Will, Cynthia |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $M=G/K$ be a compact homogeneous space and assume that $G$ and $K$ have many simple factors. We show that the topological condition of having maximal third Betti number, in the sense that $b_3(M)=s-1$ if $G$ has $s$ simple factors, so called {\it aligned}, leads to a relatively manageable algebraic structure on the isotropy representation, paving the way to the computation of Ricci curvature formulas for a large class of $G$-invariant metrics. As an application, we study the existence and classification of Einstein metrics on aligned homogeneous spaces. Comment: 37 pages |
| Databáze: | arXiv |
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